ECE 102 Engineering Computation

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1 ECE 102 Engineering Computation Phillip Wong MATLAB Vector Operations Vector Math Strings

2 Vector Operations A vector is a list of values placed in a single row or column. Each value is called an element. To create a vector from a list of values: variable_name = [ elements ] Use brackets when defining a vector. Vectors are 1-dimensional arrays. 1

3 To create a row vector: Type the list with a space or comma between each element. Example: v = [ ] v = [1,2,3,4] Use the colon operator ( :) to either Create vectors with fixed spacing between values -or- Reference a range of values within the vector 2

4 To create a row vector with constant spacing: variable_name = [m:q:n] or m:q:n m first term q spacing between terms (i.e., step value) n last term If spacing is omitted, it defaults to +1. Example: x = [0:0.5:2] y = 0:2:7 z = -2:

5 To create a row vector with constant spacing: variable_name = linspace(xf,xl,n) xf first term xl last term n number of terms Example: x = linspace(0,3,2) 0 3 y = linspace(0,3,3) z = linspace(0,3,4)

6 To create a row vector with logarithmic spacing: variable_name = logspace(x1,x2,n) X1 first decade 10 X1 X2 last decade 10 X2 N number of points between 10 X1 and 10 X2 Example: x = logspace(0,2,3) y = logspace(0,2,4)

7 To create a column vector: Type a semicolon between each element. Example: v = [1;2;3;4] Use the transpose operator ( ') to convert a row vector to a column vector Example: v = [3-1 2]' Transpose 6

8 Use parentheses with an index to access a specific element in a vector. v 1 1 Suppose v v 1 v 2 v m or v v m v m m v(k)is the k-thelement in the vector. Vector indices in MATLAB always start at one (1) Example: Let v = [ ] v(1)is 5, v(3)is 1, v(4)is 3 y = v(2)+1means yhas value -8+1=-7 7

9 To modify a specific element in a vector: Set the indexed element to a new value. Example: Let v = [ ] v(2)= v(2)= v(4) To find the current length of a vector: Use the length()function. It returns the number of elements contained in the vector. Example: Let v = [ ] L = length(v) 4 8

10 To extract a subvectorfrom a vector: Use the colon operator Example: Let v = [ ] a = v(2:4) b = v(2:3) -8 1 To extend the size of a vector: i.e., v(2), v(3), v(4) i.e., v(2), v(3) Use an index larger than the current size. Example: Let v = [3 0 2] v(4) = v(7) = Auto-fills with zeros 9

11 To create an empty vector: Use a pair of brackets with no values defined. Example: Let v = [] To concatenate a vector: Use this syntax: v = [v ele] or [ele v] Example: Let z = [1] 1 z = [z 3] 1 3 z = [2 z]

12 Vector Math Addition and subtraction: These operations follow linear algebra rules. Multiplication: Vector multiplied by a scalar Let abe a vector and kbe a scalar. Syntax: k* a (result is a vector) Example: Let a= [1 4 3] (1.5)* a

13 Vector multiplied by a vector (scalar dot product) Let aand bbe vectors of the same length. Find a b. Syntax: dot(a,b) Example: Let a= [1 4 3] and b= [5-1 2] dot(a,b) 7 Vector multiplied by a vector (vector cross product) Let aand bbe vectors of length 3. Find a b. Syntax: cross(a,b) Example: Let a= [1 4 3] and b= [5-1 2] cross(a,b)

14 Element-by-element (EBE) operations: By preceding certain operators with a period, EBE is done instead of the normal operation. Vector multiplied by a vector (EBE) Leta = [a 1 a 2 a m ] and b = [b 1 b 2 b m ] a.* b a 1 b 1 a 2 b 2 a m b m Example: Let a= [1 4 3] and b= [5-1 2] a.* b Note: This also applies to column vectors. 13

15 Vector divided by a vector (EBE) Leta = [a 1 a 2 a m ] and b = [b 1 b 2 b m ] a./ b a 1 /b 1 a 2 /b 2 a m /b m Example: Let a= [1 4 3] and b= [5-1 2] a./ b Vector raised to a scalar power (EBE) Leta = [a 1 a 2 a m ] and kbe a scalar a.^ k (a 1 ) k (a 2 ) k (a m ) k Example: Let a= [-2 4 3] a.^

16 Vector raised to a vector power (EBE) Leta = [a 1 a 2 a m ] and b = [b 1 b 2 b m ] b 1 b 2 b m a.^ b (a 1 ) (a 2 ) (a m ) Example: Let a= [-2 4 3] and b= [3-1 2] a.^ b Vector as a function argument (EBE) Leta = [a 1 a 2 a m ] f (a) f (a 1 ) f (a 2 ) f (a m ) Example: Let a= [1 4 3] sin(a)

17 Summary of Vector Operators Addition or unary plus + Subtraction or unary minus - Vector Multiplication * Vector Division / Array Multiplication (EBE).* Array Division (EBE)./ Array Power (EBE).^ 16

18 Strings A string can be considered a vector of characters. Type the characters within single quotes. To embed a single quote within a string, type two consecutive single quotes. Example: 'Hello', 'Good bye 12? ' name = 'George Smith' disp(name) George Smith disp(name(1:6)) George x=['hi, ' name] Hi, George Smith 17

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